The function f(x) = 3x - 5 for x 3 and = c for x = 3 and is continuous at x = 3, if c is equal to

Question

The function f(x) = 3x - 5 for x < 3 and - x + 1 for x > 3 and = c for x = 3 and is continuous at x = 3, if c is equal to (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

lim x→ 3- f(x) = lim x→ 3 (3x -5) = 9 - 5 = 4 lim x→ 3+ f(x) = lim x→ 3 (x+1) = 3+ 1 = 4 ∴ lim x→ 3 f(x) = 4 = f(3) = c ∴ c= 4 [ ∵ f is continuous at x = 3]

Q. The function $f (x) = 3 x - 5$ for $x < 3$ and $- x + 1$ for $x > 3$ and = $c$ for $x$ = 3 and is continuous at $x$ = 3, if $c$ is equal to

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4

$lim_{x \to 3 -} f (x) = lim_{x \to 3} (3 x - 5) = 9 - 5 = 4$
$lim_{x \to 3 +} f (x) = lim_{x \to 3} (x + 1) = 3 + 1 = 4$
$∴$ $lim_{x \to 3} f (x) = 4 = f (3) = c ∴ c = 4$
[ $∵ f$ is continuous at $x$ = 3]

Q. The function f(x)=3x−5 for x<3 and −x+1 for x>3 and = c for x = 3 and is continuous at x = 3, if c is equal to

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4

limx→3−​f(x)=limx→3​(3x−5)=9−5=4 limx→3+​f(x)=limx→3​(x+1)=3+1=4 ∴ limx→3​f(x)=4=f(3)=c∴c=4 [ ∵f is continuous at x = 3]

Q. The function $f (x) = 3 x - 5$ for $x < 3$ and $- x + 1$ for $x > 3$ and = $c$ for $x$ = 3 and is continuous at $x$ = 3, if $c$ is equal to

$lim_{x \to 3 -} f (x) = lim_{x \to 3} (3 x - 5) = 9 - 5 = 4$
$lim_{x \to 3 +} f (x) = lim_{x \to 3} (x + 1) = 3 + 1 = 4$
$∴$ $lim_{x \to 3} f (x) = 4 = f (3) = c ∴ c = 4$
[ $∵ f$ is continuous at $x$ = 3]